Semiclassical wavefunctions for open quantum billiards

TL;DR

This paper introduces a semiclassical approximation method for scattering wavefunctions in open quantum billiards, demonstrating high accuracy and potential applications in leaky systems and decoherence scenarios.

Contribution

It develops a new semiclassical approach based on Feynman path integrals for open quantum billiards, improving accuracy over previous methods.

Findings

High numerical accuracy in open rectangular billiards

Convergence controlled by path length or dwell time

Potential applications in leaky and decoherent systems

Abstract

We present a semiclassical approximation to the scattering wavefunction $\Psi(\mathbf{r},k)$ for an open quantum billiard which is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numerical accuracy for the open rectangular billiard and show that the convergence of the semiclassical wavefunction to the full quantum state is controlled by the path length or equivalently the dwell time. Possible applications include leaky billiards and systems with decoherence present.